A Derivation of Proca Equations on Cantor Sets: A Local Fractional Approach

Christianto, Victor; Rahul, Biruduganti

doi:10.18052/www.scipress.com/BMSA.10.48

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A Derivation of Proca Equations on Cantor Sets: A Local Fractional Approach

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Abstract:

In a recent paper published at Advances in High Energy Physics (AHEP) journal, Yang Zhao et al. derived Maxwell equations on Cantor sets from the local fractional vector calculus. It can be shown that Maxwell equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Using the same approach, elsewhere Yang, Baleanu & Tenreiro Machado derived systems of Navier-Stokes equations on Cantor sets. However, so far there is no derivation of Proca equations on Cantor sets. Therefore, in this paper we present for the first time a derivation of Proca equations and GravitoElectroMagnetic (GEM) Proca-type equations on Cantor sets. Considering that Proca equations may be used to explain electromagnetic effects in superconductor, We suggest that Proca equations on Cantor sets can describe electromagnetic of fractal superconductors; besides GEM Proca-type equations on Cantor sets may be used to explain some gravitoelectromagnetic effects of superconductor for fractal media. It is hoped that this paper may stimulate further investigations and experiments in particular for fractal superconductor. It may be expected to have some impact to fractal cosmology modeling too.

Info:

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 10)

Pages:

48-56

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.10.48

Citation:

V. Christianto and B. Rahul, "A Derivation of Proca Equations on Cantor Sets: A Local Fractional Approach", Bulletin of Mathematical Sciences and Applications, Vol. 10, pp. 48-56, 2014

Online since:

November 2014

Authors:

Victor Christianto, Biruduganti Rahul

Keywords:

Cantor Sets, Fractal Cosmology, Gravitoelectromagnetic Effect, Local Fractional Vector Calculus, Maxwell Equations, Proca Equations, Superconductor

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Creative Commons Attribution 4.0 International License

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Cited By:

[1] D. Baleanu, H. Khan, H. Jafari, R. Khan, "On the Exact Solution of Wave Equations on Cantor Sets", Entropy, Vol. 17, p. 6229, 2015

DOI: https://doi.org/10.3390/e17096229

[2] H. Jassim, "The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator", Abstract and Applied Analysis, Vol. 2016, p. 1, 2016

DOI: https://doi.org/10.1155/2016/2913539